CSI 2101 Study Guide - Quiz Guide: Extended Euclidean Algorithm, Euclidean Algorithm, Public-Key Cryptography

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This solution is prepared by the professor for use of students enrolled in the course in the winter. No part of this document may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without prior written permission from the instructor. Rsa and induction proofs: (10=3+4+3 marks) consider the rsa cryptosystem where letters a to z are encoded to two-digit numbers 00 to 25 respectively. Show your steps and derive the number that represents the encoded message. 1314299 mod 4757 = 3411. (b) calculate bob"s private key, using the knowledge that n = 67 71. Now we work backwards to get the inverse of 299. 29 = 299 2 135 = 299 2 (4620 15 299) = 31 299 2 4620. 10 = 29 1 19 = (31 299 2 4620) (9 4620 139 299) = 170 299 11 4620.

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